Camilla Felisetti (Università di Modena e Reggio Emilia)

Abstract: Intersection cohomology is a topological notion adapted to the description of singular topological spaces, and the Decomposition Theorem for algebraic maps is a key tool in the subject. The study of the intersection cohomology of the moduli spaces of semistable bundles on Riemann surfaces began in the 80’s with the works of Frances Kirwan. Motivated by the results of Mozgovoy and Reineke, in joint work in progress with Andras Szenes and Olga Trapeznikova, we aim to give a complete description of these structures via a detailed analysis of the Decomposition Theorem applied to a certain map from parabolic bundles. We provide a new formula for the intersection Betti numbers of these moduli spaces, which has an explicit geometric meaning. In the first part of the talk, I will give an introduction to the subject and to the tools appearing in our work in, while in the second describe the results obtained together with a sketch of the proofs.